Seite - 164 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 5 TheVP-SoCprofileduringtheC/2rateCCchargingprocess is showninFigure3. Since in the HEV/EVapplication,batteries seldomwork in theextremely loworhighSoCs, thevoltageprofile from10%–90%SoC is covered. It canbeobservedfromFigure3 that thepolarizationvoltage increases dramatically in Stage I (10%–18%SoC), then it declines slowly and shows a concave shape curve in Stage II, with the localminimumvalue at around 30% SoC. During Stage III (40%–70% SoC), thepolarizationvoltagebecomesrelativelystable.After that (70%–90%SoC), thepolarizationvoltage risessharply. 6R& $ % & ' ( ) ĉ Ċ ċ Č Figure3.VPversusSoCunderconstant-current (CC)charging. Thevariationof thepolarizationvoltageduring the aboveSoC range is closely related to the internal electrochemical reaction process during charging. In the initial SoC region, a relatively largeamountofenergy isneededto formthenucleationonthesurfacesof theelectrodes; thus, the polarizationvoltage increasesquickly.Once thenucleiare formed, the following lithiumions’ removal processneeds less energy. This explains the concave shapevoltage curveoccurring from18%SoC to40%SoC.While in the lastchargingstage, the lithium-ionconcentration increases in thenegative materials. Hence, a largeamountofenergy isneeded to insert the lithiumions,which leads to the obviousgrowthof thepolarizationvoltage in thehighSoC region. Thedetailedexplanationfor the electrochemical reactionmechanismoccurringduringtheCCchargingprocesscanbe foundin [28,32]. AsmentionedinSection2, themodelparametersareestimatedthroughfitting themeasureddata either fromthepulse-chargingperiodor therestperiod. Inorder toselect theproperexperimental datasetsthatcanbetterdescribethechargingcharacteristicofthebattery, theprofilesofthepolarization voltageduring thepulse-charging and the following rest periods,which are also calculated from Equation (10), are compared in Figure 4. Figure 4a shows the polarization voltage under the pulse-chargingexcitation,andFigure4bplots theabsolutevaluesof thepolarizationvoltageduring the followingrest. It canbeseen frombothfigures that theshapeof thepolarizationvoltagecurve stronglydependsontheSoC. InFigure4a, it isobvious that thefinalvalueof thepolarizationvoltage obtainedfrom26%–28%SoC is the lowest,which is similar topointCinFigure3. Inaddition, thefinal valuesof thevoltagecurvesobtained from18%–20%SoCand50%–52%SoCarealmost coincident with each other, which approximatelymatches the corresponding parts (point B andpointD) in Figure 3. Meanwhile, the relations among the final voltage values collected from14%–16% SoC, 60%–62%SoCand80%–82%SoCarealso identical to therelationsamongpointA,pointEandpoint F inFigure3, respectively. Hence, it canbesummarized fromFigure4a that thefinalvaluesof the polarizationvoltage obtained fromdifferent pulse-chargingperiods are approximately consistent with thecorrespondingpoints inFigure3.While inFigure4b, thevariation trendof thepredicted stable voltage values differs greatly compared to the results in Figure 4a. This is because in the pulse-chargingperiod, the ionmigration isdrivenbyexternal electric potential. While in the rest period, the transportof ions ismainlydominatedbydiffusion,owingto theconcentrationgradient. Thedetailedexplanationof theelectrochemical reactionsoccurringunderdifferent loadcurrenthas beendiscussed in [21,45]. 164